TSTP Solution File: SEU146+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU146+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 16:22:45 EDT 2023

% Result   : Theorem 0.15s 0.50s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   44 (   8 unt;  10 typ;   0 def)
%            Number of atoms       :   87 (  29 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   83 (  30   ~;  39   |;   7   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (   2 sgn;  29   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    in: ( $i * $i ) > $o ).

tff(decl_23,type,
    subset: ( $i * $i ) > $o ).

tff(decl_24,type,
    empty_set: $i ).

tff(decl_25,type,
    empty: $i > $o ).

tff(decl_26,type,
    singleton: $i > $i ).

tff(decl_27,type,
    set_difference: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

fof(l3_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => ( in(X3,X1)
        | subset(X1,set_difference(X2,singleton(X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).

fof(t37_xboole_1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(reflexivity_r1_tarski,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(l4_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

fof(l2_zfmisc_1,axiom,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(t3_xboole_1,axiom,
    ! [X1] :
      ( subset(X1,empty_set)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

fof(t2_xboole_1,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).

fof(c_0_8,plain,
    ! [X10,X11,X12] :
      ( ~ subset(X10,X11)
      | in(X12,X10)
      | subset(X10,set_difference(X11,singleton(X12))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).

fof(c_0_9,plain,
    ! [X19,X20] :
      ( ( set_difference(X19,X20) != empty_set
        | subset(X19,X20) )
      & ( ~ subset(X19,X20)
        | set_difference(X19,X20) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).

cnf(c_0_10,plain,
    ( in(X3,X1)
    | subset(X1,set_difference(X2,singleton(X3)))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,plain,
    ( set_difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_12,plain,
    ! [X17] : subset(X17,X17),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,singleton(X2))
      <=> ( X1 = empty_set
          | X1 = singleton(X2) ) ),
    inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).

fof(c_0_14,plain,
    ! [X8,X9] :
      ( ( ~ subset(singleton(X8),X9)
        | in(X8,X9) )
      & ( ~ in(X8,X9)
        | subset(singleton(X8),X9) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).

cnf(c_0_15,plain,
    ( subset(X1,empty_set)
    | in(X2,X1)
    | ~ subset(X3,singleton(X2))
    | ~ subset(X1,X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_17,plain,
    ! [X6,X7] :
      ( ( subset(X6,X7)
        | X6 != X7 )
      & ( subset(X7,X6)
        | X6 != X7 )
      & ( ~ subset(X6,X7)
        | ~ subset(X7,X6)
        | X6 = X7 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).

fof(c_0_18,negated_conjecture,
    ( ( esk1_0 != empty_set
      | ~ subset(esk1_0,singleton(esk2_0)) )
    & ( esk1_0 != singleton(esk2_0)
      | ~ subset(esk1_0,singleton(esk2_0)) )
    & ( subset(esk1_0,singleton(esk2_0))
      | esk1_0 = empty_set
      | esk1_0 = singleton(esk2_0) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).

cnf(c_0_19,plain,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    ( subset(X1,empty_set)
    | in(X2,X1)
    | ~ subset(X1,singleton(X2)) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

fof(c_0_21,plain,
    ! [X21] :
      ( ~ subset(X21,empty_set)
      | X21 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( subset(esk1_0,singleton(esk2_0))
    | esk1_0 = empty_set
    | esk1_0 = singleton(esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    ( subset(singleton(X1),X2)
    | subset(X2,empty_set)
    | ~ subset(X2,singleton(X1)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,plain,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( singleton(esk2_0) = esk1_0
    | esk1_0 = empty_set
    | ~ subset(singleton(esk2_0),esk1_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( esk1_0 != singleton(esk2_0)
    | ~ subset(esk1_0,singleton(esk2_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,negated_conjecture,
    ( singleton(esk2_0) = esk1_0
    | esk1_0 = empty_set ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_25]),c_0_26]) ).

fof(c_0_29,plain,
    ! [X18] : subset(empty_set,X18),
    inference(variable_rename,[status(thm)],[t2_xboole_1]) ).

cnf(c_0_30,negated_conjecture,
    ( esk1_0 != empty_set
    | ~ subset(esk1_0,singleton(esk2_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_31,negated_conjecture,
    esk1_0 = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16])]) ).

cnf(c_0_32,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_32])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SEU146+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Wed Aug 23 13:06:56 EDT 2023
% 0.11/0.30  % CPUTime  : 
% 0.15/0.49  start to proof: theBenchmark
% 0.15/0.50  % Version  : CSE_E---1.5
% 0.15/0.50  % Problem  : theBenchmark.p
% 0.15/0.50  % Proof found
% 0.15/0.50  % SZS status Theorem for theBenchmark.p
% 0.15/0.50  % SZS output start Proof
% See solution above
% 0.15/0.51  % Total time : 0.008000 s
% 0.15/0.51  % SZS output end Proof
% 0.15/0.51  % Total time : 0.010000 s
%------------------------------------------------------------------------------